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If the system of equations

3x + y = a

2x + 5y = 2a

has a solution (x,y) when x = -2, compute a

 Jun 22, 2022
 #1
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We can rewrite the system of equations by replacing \(x\) with \(-2\) to get

 

\(y-6=a\)

\(5y-10=2a\).

 

Multiplying the first equation by \(2\), we have \(2y-12=2a\).

 

Subtracting this from the second equation says that \(3y+2=0\), so therefore \(y=-2/3\), and so \(a=-20/3\).

 Jun 22, 2022

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